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Jackson Type Theorems for Compact Rank 1 Symmetric Spaces

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References

  1. Nikol'skiľ S. M. and Lizorkin P. I., “Approximation by spherical polynomials,” Trudy Inst. Mat. Akad. Nauk SSSR, 166, 186–200 (1984).

    Google Scholar 

  2. Nikol'skiľ S. M. and Lizorkin P. I., “Approximation of functions on the sphere,” Izv. Akad. Nauk SSSR Ser. Mat., 51, No. 3, 635–651 (1987).

    Google Scholar 

  3. Rustamov Kh. P., “On approximation of functions on the sphere,” Izv. Ros. Akad. Nauk Ser. Mat., 57, No. 5, 127–148 (1993).

    Google Scholar 

  4. Besse A. L., Manifolds All Whose Geodesics Are Closed [Russian translation], Mir, Moscow (1981).

    Google Scholar 

  5. Tikhomirov V. M. “Approximation theory,” in: Contemporary Problems of Mathematics. Fundamental Trends [in Russian], VINITI, Moscow, 1987, 34, Chapter 4, § 2 (Itogi Nauli i Tekhniki).

    Google Scholar 

  6. Kamzolov A. I., “On the Riesz interpolation formula and the Bernstein inequality for functions on homogeneous spaces,” Mat. Zametki, 35, No. 6, 967–978 (1974).

    Google Scholar 

  7. Ragozin D. L., “Polynomial approximation on compact manifolds and homogeneous spaces,” Trans. Amer. Math. Soc., 150, 41–53 (1971).

    Google Scholar 

  8. Ivanov V. A., “On the Bernstein-Nikol'skiľ and Favard inequalities on compact homogeneous spaces of rank 1,” Uspekhi Mat. Nauk, 38, No. 3, 179–180 (1983).

    Google Scholar 

  9. Luoqung L., “Riesz means on compact Riemannian symmetric spaces,” Math. Nachr., 188, 227–242 (1994).

    Google Scholar 

  10. Helgason S., Groups and Geometric Analysis [Russian translation], Mir, Moscow (1987).

    Google Scholar 

  11. Helgason S., Differential Geometry and Symmetric Spaces [Russian translation], Mir, Moscow (1964).

    Google Scholar 

  12. Nikol'skiľ S. M., Approximation of Functions in Several Variables and Embedding Theorems [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  13. Terekhin A. P., “Uniform approximation on a sphere of odd-dimensional space by algebraic polynomials,” Mat. Zametki, 41, No. 3, 333–341 (1987).

    Google Scholar 

  14. Lizorkin P. I., “Approximation of functions over the sphere σ. On the spaces B α p,q(σ),” Dokl. Akad. Nauk, 331, No. 5, 555–558 (1993).

    Google Scholar 

  15. Platonov S. S., “On Jackson type theorems on a compact rank 1 symmetric space,” Dokl. Akad. Nauk, 357, No. 4, 445–448 (1997).

    Google Scholar 

  16. Platonov S. S., “On the Nikol'skiľ-Besov classes on compact rank 1 symmetric spaces,” Trudy Petrozavodsk. Univ. Ser. Mat., 1, No. 3, 153–172 (1996).

    Google Scholar 

  17. Platonov S. S., “Approximation of functions on compact rank 1 symmetric spaces,” Mat. Sb., 188, No. 5, 113–130 (1997).

    Google Scholar 

  18. Dzyadyk V. K., Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).

    Google Scholar 

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Platonov, S.S. Jackson Type Theorems for Compact Rank 1 Symmetric Spaces. Siberian Mathematical Journal 42, 119–130 (2001). https://doi.org/10.1023/A:1004801812016

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